Chelsea dropped two points in their bid for a Champions League return as Southampton saw out a stalemate at Stamford Bridge.
Eden Hazard was twice denied by Saints goalkeeper Angus Gunn and Alvaro Morata had a strike ruled out for offside as the Blues' lack of attacking precision was evident once more in the goalless draw.
Chelsea reached the turn of the year in fourth place, five points clear of Arsenal, but the Gunners' win over Fulham on New Year's Day, plus the stubbornness of relegation-threatened Saints, cut their advantage to three points.
One of Southampton's eight changes following the loss to Manchester City came in goal, where Gunn replaced Alex McCarthy to make his Premier League debut.
The 22-year-old used his head to repel Chelsea's best chance of the first half, after Antonio Rudiger's lofted ball had found Hazard.
Hazard struck a bouncing ball from point-blank range, with Gunn making the save at the near post.
That chance came after 34 minutes and even prior to that it had looked like the direct route would be most profitable for the hosts.
Cesar Azpilicueta's pass was just glanced on by Alvaro Morata, who came in for the injured Olivier Giroud as Chelsea's sole change following last Sunday's win at Crystal Palace.
Saints were proving stubborn opponents, content to play on the break, with Danny Ings heading over a Cedric Soares cross after 15 minutes.
Saints' play was robust, with Oriol Romeu requiring treatment for a cut head and Jan Bednarek booked for a cynical foul on Morata.
Willian was then clattered by Maya Yoshida and with Pedro and Callum Hudson-Odoi already injured on the sidelines, Maurizio Sarri was taking no chances. The Brazilian was replaced by Ruben Loftus-Cheek.
Chelsea had a further opportunity before the break, which concluded when Ross Barkley found Morata but the striker's poor shot was blocked by Yan Valery for a corner.
Shane Long replaced Ings at half-time for Southampton, who went close when Stuart Armstrong had a shot turned around the post by Kepa Arrizabalaga.
Saints appeared more confident in the second half, but they also had to be on their guard.
Hazard was denied by Gunn again after 58 minutes. The Belgian cut in from the left and fired at the goalkeeper, who palmed the ball away.
With Chelsea needing more creativity, Cesc Fabregas came on. Instead of replacing Jorginho, he came on alongside him, replacing Barkley to play in a more advanced role for the former Arsenal midfielder's 500th appearance in English football.
Fabregas thought he had unlocked the Saints defence within moments of his introduction.
He found Morata, who netted after 70 minutes, but the strike was ruled out for offside with replays suggesting the call was marginal.
The midfielder again was the creator as Chelsea - and Morata - came close once more.
The Spaniard threaded a pass to Loftus-Cheek, who cut inside and fed Morata but The striker's shot was unconvincing and straight at Gunn.
Hazard then found Fabregas, but Saints crowded out any shooting opportunity and cleared.
Marcos Alonso fell in the penalty area in stoppage time, more in desperation than expectation of a spot-kick, and then had a shot saved by Gunn as Saints held on to leave Chelsea frustrated and take away a valuable point.